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On the openness of continuous averagings

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Abstract

A metrizable compact convex set K is stable if and only if continuous averaging on K is open.

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References

  1. Chang, S. M.: On continuous image averaging of probability measures. Pacific J. Math. 65 (1976), 13–17.

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  2. Clausing, A. and Papadopoulou, S.:Stable convex sets and extremal operators. Math. Ann. (to appear).

  3. Michael, E.: A survey of continuous selections. Lecture Notes in Math. Vol. 171 (1970), 54–57.

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  4. O'Brien, R. C.: On the openness of the barycentre map. Math. Ann. 223 (1976), 207–212.

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Authors and Affiliations

  1. Mathematisches Institut der Universität, Bismarckstr. 1 1/2, D-8520, Erlangen, Fed. Rep. of Germany

    A. Clausing

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  1. A. Clausing
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Clausing, A. On the openness of continuous averagings. Manuscripta Math 24, 1–7 (1978). https://doi.org/10.1007/BF01168559

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  • DOI: https://doi.org/10.1007/BF01168559

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